This is a casebook of math problems from industry. The source code and out
put are listed. The problems solved range from Algebra thru Differential e

quations. Problems include Initial-Value, Boundary-Value, Inverse, etc. T
he equations may be non-linear, any degree, any order, implicit, etc. Code
s are very short, normally 30 lines or less PLUS one's equations and someti
mes plot code. Number of equations may be from 1 to 1,000 or more.
Teaching engineering, science and/or operations research student?s
problem solving techniques that will work in the future is not easy. Probl
em solving requires a broad based knowledge in math and science as well as
discernment and flexibility to challenge the way it has always been done in
the past. Generally, an objective driven design will yield the best desig
n in the least amount of time. Companies need engineers trained in setting
objectives before they begin the time-consuming process of formulating and
testing new concepts and designs.
Our textbook titled "Engineering Design Optimization using Calculus Level M
ethods: A Casebook Approach", http://fortranCalculus.info/textbooks , consi
ders design from the pragmatic concerns of industry. It utilizes casebook
studies of math problems with their solutions in real life situations. Bec
ause it encourages students to view themselves as part of the design team,
this text is the next best thing to an on-the-job training. It shows how s
etting objectives to problem solving assignments can help students complete
work quickly and efficiently, but it also stresses that while every situat
ion is different, the approach remains the same: objective-driven engineers
state a math model and an objective function for a given problem while lea
ving the solving to a calculus-level computer language/compiler.
Our textbook attempts to fill a gap in educational material in the mathemat
ical problem solving arena. Traditional texts leave students in a simulati
on thinking mode. Simulations require many computer runs causing delays in
solution and little gain, if any, in problem understanding. Simulations r
equire a numerical algorithm to be meshed with their math model. In such f
orm, math models are hard to recognize and discuss. Besides slowing their
understanding, users lose confidence in program solutions.
This textbook tries to move today?s thinking from solving one probl
em at a time, to solving all of their project?s problems at once wh
ile tweaking parameters in order to achieve an optimum solution. This requ
ires Calculus-level thinking. An analogy might be thinking in terms of Mac
hine code, one bit at a time. Today, computer simulations have people thin
king in terms of Algebraic code, one problem at a time. We are trying to m
ove people to Calculus-level code, solving entire projects at a time. This
will reduce development time and improve accuracy of their math models.
History: NASA funded the development of the first Calculus-level language t
hrough TRW called Prose. Prose became available to the public in 1974 thro
ugh a national computer time-sharing network. Prose ran on large Control D
ata Corporation (CDC) 6600 computers. Automatic differentiation and operat
or overloading were key technologies for this project. I taught the Prose
language to Engineers & Scientists in the San Francisco Bay Area from 1975
through 1979. Most national time-sharing computer networks died in the 198
0s and thus went Prose. FortranCalculus is the next Calculus language on t
he horizon. It is in testing mode now and will soon be released on the web
.
Book goal: get users thinking outside their box. For example, the Oil
Refinery problem shows how one could solve oil production for one distillat
ion unit, or one plant, or an entire corporation (i.e. many refineries) all
at once! This may consist of one, 100, or 10,000 differential equations w
hile searching for the best refinery(s) to produce products that have pollu
tion by-products. The goal is to minimize pollution by choosing the locati
on where each product is produced. Solve the whole problem in one run not
just part of problem.
One reviewer wrote: "The most important pedagogical value the book could de
liver is a sound grounding in calculus level thinking for engineering desig
n optimization. This approach is as significant for engineering/science as
object oriented programming has been for computer science.
Independent access to a computer system running the calculus tools would fr
ee the reader from having to attend a class. This would open up the market
for the book quickly to practicing engineers."
Our software, http://fortranCalculus.info/apps/fc-compiler.html , is free f
or 10 days. Try some demos and solve your own math model problems. Try va
rying your math model to find the best one ... easy to do :)
Phil

Log in

Polytechforum.com is a website by engineers for engineers. It is not affiliated with any of manufacturers or vendors discussed here.
All logos and trade names are the property of their respective owners.